For (2), you know the force on Mars by the sun is given by
$\displaystyle F=GmM/R=mv^2/2$
where the second equality is using the fact that mars is experiencing centripetal acceleration around the sun. From there you can use the fact that
$\displaystyle v=d/t=2\pi R/T$
where T is the period and R is the radius of Mars' orbit.

Plugging that expression for v into the top equation gives you an equation where you know everything except M, the mass of the sun.